Such a tire building apparatus is described in DE 42 20 490 A1. In this known tire building apparatus one piston tube, which extends over the length of the pressure roll and is chargeable with a pressure means, is arranged in the space between the shaft and the recess, thus in the head stroke space and the foot stroke space. Using piston tubes has disadvantages, however. It is possible, for example, that after repeated charging of the piston tubes, the elasticity of the piston tubes decreases or that holes develop in the piston tubes, so that the action of the pressure roll is adversely affected and the piston tubes have to be constantly replaced. In addition, it is very difficult to control each disc separately and although this possibility is mentioned in DE 42 20 490 A1, no further embodiment thereof is described.